Two-stage cluster samples with judgment post-stratification

Estimation of the population mean or total in a clustered population can be done using a two-stage sampling design. Here we present design-unbiased estimators and their variances and approximate confidence intervals for the population mean and total for sampling designs in which a cluster sampling is undertaken at each stage as either judgment post-stratified (JPS) or simple random sampling (SRS). SRS is performed without replacement, while JPS designs can be implemented with or without replacement. The efficiency of JPS designs relative to the SRS design is investigated. The proposed estimators have smaller variances under JPS than the two-stage SRS design. The gain in efficiency depends on the intra-cluster correlation coefficient and the sampling design choices at each stage. To achieve a fixed cost, the optimal sample sizes are derived for each stage by maximizing the information content of the sample. The proposed sampling designs and estimators are illustrated with a real-life agricultural sampling task for vineyard management.